Using R for Analyzing Practical Data - Basic Level
HUYNH THIEN
07/04/2024
housing_prices = read.csv("C:/Users/25047390/OneDrive - UTS/Desktop/module 10/Housing_prices.csv")Observations
housing_prices## ID river rooms price age industry ptratio low_ses
## 1 1 No 6-room 21.6 78.9 7.07 17.8 9.14
## 2 2 No 7-room 34.7 61.1 7.07 17.8 4.03
## 3 3 No 7-room 33.4 45.8 2.18 18.7 2.94
## 4 4 No 7-room 36.2 54.2 2.18 18.7 5.33
## 5 5 No 6-room 28.7 58.7 2.18 18.7 5.21
## 6 6 No 6-room 20.4 61.8 8.14 21.0 8.26
## 7 7 No 6-room 18.2 84.5 8.14 21.0 10.26
## 8 8 No 6-room 19.9 56.5 8.14 21.0 8.47
## 9 9 No 6-room 23.1 29.3 8.14 21.0 6.58
## 10 10 No 6-room 17.5 81.7 8.14 21.0 14.67
## 11 11 No 5-room 20.2 36.6 8.14 21.0 11.69
## 12 12 No 6-room 18.2 69.5 8.14 21.0 11.28
## 13 13 No 6-room 13.6 98.1 8.14 21.0 21.02
## 14 14 No 6-room 19.6 89.2 8.14 21.0 13.83
## 15 15 No 6-room 15.2 91.7 8.14 21.0 18.72
## 16 16 No 6-room 14.5 100.0 8.14 21.0 19.88
## 17 17 No 6-room 15.6 94.1 8.14 21.0 16.30
## 18 18 No 6-room 13.9 85.7 8.14 21.0 16.51
## 19 19 No 6-room 16.6 90.3 8.14 21.0 14.81
## 20 20 No 6-room 14.8 88.8 8.14 21.0 17.28
## 21 21 No 6-room 18.4 94.4 8.14 21.0 12.80
## 22 22 No 7-room 21.0 87.3 8.14 21.0 11.98
## 23 23 No 6-room 12.7 94.1 8.14 21.0 22.60
## 24 24 No 6-room 14.5 100.0 8.14 21.0 13.04
## 25 25 No 6-room 13.2 82.0 8.14 21.0 27.71
## 26 26 No 6-room 13.1 95.0 8.14 21.0 18.35
## 27 27 No 6-room 13.5 96.9 8.14 21.0 20.34
## 28 28 No 6-room 18.9 68.2 5.96 19.2 9.68
## 29 29 No 6-room 20.0 61.4 5.96 19.2 11.41
## 30 30 No 6-room 21.0 41.5 5.96 19.2 8.77
## 31 31 No 6-room 24.7 30.2 5.96 19.2 10.13
## 32 32 No 7-room 26.6 2.9 6.91 17.9 4.84
## 33 33 No 6-room 25.3 6.6 6.91 17.9 5.81
## 34 34 No 6-room 24.7 6.5 6.91 17.9 7.44
## 35 35 No 6-room 21.2 40.0 6.91 17.9 9.55
## 36 36 No 6-room 19.3 33.8 6.91 17.9 10.21
## 37 37 No 6-room 20.0 33.3 6.91 17.9 14.15
## 38 38 No 6-room 16.6 85.5 6.91 17.9 18.80
## 39 39 No 5-room 14.4 95.3 6.91 17.9 30.81
## 40 40 No 6-room 19.4 62.0 6.91 17.9 16.20
## 41 41 No 6-room 24.2 6.6 10.81 19.2 6.72
## 42 42 No 6-room 21.7 17.5 10.81 19.2 9.88
## 43 43 No 6-room 22.8 7.8 10.81 19.2 5.52
## 44 44 No 6-room 23.4 6.2 10.81 19.2 7.54
## 45 45 No 6-room 24.1 6.0 12.83 18.7 6.78
## 46 46 No 6-room 21.4 45.0 12.83 18.7 8.94
## 47 47 No 6-room 20.0 74.5 12.83 18.7 11.97
## 48 48 No 6-room 20.8 45.8 12.83 18.7 10.27
## 49 49 No 6-room 21.2 53.7 12.83 18.7 12.34
## 50 50 No 6-room 20.3 36.6 12.83 18.7 9.10
## 51 51 No 6-room 23.9 48.0 4.49 18.5 9.62
## 52 52 No 7-room 26.6 56.1 4.49 18.5 6.53
## 53 53 No 6-room 22.5 45.1 4.49 18.5 12.86
## 54 54 No 6-room 22.2 56.8 4.49 18.5 8.44
## 55 55 No 7-room 23.6 86.3 3.41 17.8 5.50
## 56 56 No 7-room 28.7 63.1 3.41 17.8 5.70
## 57 57 No 6-room 22.6 66.1 3.41 17.8 8.81
## 58 58 No 6-room 22.0 73.9 3.41 17.8 8.20
## 59 59 No 7-room 28.4 57.8 2.89 18.0 6.65
## 60 60 No 6-room 21.4 69.6 2.89 18.0 11.34
## 61 61 No 7-room 38.7 76.0 2.89 18.0 4.21
## 62 62 No 7-room 43.8 36.9 2.89 18.0 3.57
## 63 63 No 7-room 33.2 62.5 2.89 18.0 6.19
## 64 64 No 7-room 27.5 79.9 8.56 20.9 9.42
## 65 65 No 7-room 26.5 71.3 8.56 20.9 7.67
## 66 66 No 6-room 18.6 85.4 8.56 20.9 10.63
## 67 67 No 6-room 19.3 87.4 8.56 20.9 13.44
## 68 68 No 6-room 20.1 90.0 8.56 20.9 12.33
## 69 69 No 6-room 19.5 96.7 8.56 20.9 16.47
## 70 70 No 6-room 19.5 91.9 8.56 20.9 18.66
## 71 71 No 6-room 20.4 85.2 8.56 20.9 14.09
## 72 72 No 6-room 19.8 97.1 8.56 20.9 12.27
## 73 73 No 6-room 19.4 91.2 8.56 20.9 15.55
## 74 74 No 6-room 21.7 54.4 8.56 20.9 13.00
## 75 75 No 7-room 22.8 81.6 10.01 17.8 10.16
## 76 76 No 6-room 18.8 92.9 10.01 17.8 16.21
## 77 77 No 6-room 18.7 95.4 10.01 17.8 17.09
## 78 78 No 6-room 18.5 84.2 10.01 17.8 10.45
## 79 79 No 6-room 18.3 88.2 10.01 17.8 15.76
## 80 80 No 6-room 21.2 72.5 10.01 17.8 12.04
## 81 81 No 6-room 19.2 82.6 10.01 17.8 10.30
## 82 82 No 6-room 20.4 73.1 10.01 17.8 15.37
## 83 83 No 6-room 19.3 65.2 10.01 17.8 13.61
## 84 84 No 6-room 22.0 69.7 25.65 19.1 14.37
## 85 85 No 6-room 20.3 84.1 25.65 19.1 14.27
## 86 86 No 6-room 20.5 92.9 25.65 19.1 17.93
## 87 87 No 6-room 17.3 97.0 25.65 19.1 25.41
## 88 88 No 6-room 18.8 95.8 25.65 19.1 17.58
## 89 89 No 6-room 21.4 88.4 25.65 19.1 14.81
## 90 90 No 6-room 15.7 95.6 25.65 19.1 27.26
## 91 91 No 6-room 16.2 96.0 21.89 21.2 17.19
## 92 92 No 6-room 18.0 98.8 21.89 21.2 15.39
## 93 93 No 6-room 14.3 94.7 21.89 21.2 18.34
## 94 94 No 6-room 19.2 98.9 21.89 21.2 12.60
## 95 95 No 6-room 19.6 97.7 21.89 21.2 12.26
## 96 96 No 6-room 23.0 97.9 21.89 21.2 11.12
## 97 97 No 6-room 18.4 95.4 21.89 21.2 15.03
## 98 98 No 6-room 15.6 98.4 21.89 21.2 17.31
## 99 99 No 6-room 18.1 98.2 21.89 21.2 16.96
## 100 100 No 6-room 17.4 93.5 21.89 21.2 16.90
## 101 101 No 6-room 17.1 98.4 21.89 21.2 14.59
## 102 102 No 6-room 13.3 98.2 21.89 21.2 21.32
## 103 103 No 6-room 17.8 97.9 21.89 21.2 18.46
## 104 104 No 6-room 14.0 93.6 21.89 21.2 24.16
## 105 105 No 5-room 14.4 100.0 21.89 21.2 34.41
## 106 106 Yes 5-room 13.4 100.0 19.58 14.7 26.82
## 107 107 No 5-room 15.6 100.0 19.58 14.7 26.42
## 108 108 No 4-room 11.8 97.8 19.58 14.7 29.29
## 109 109 No 6-room 13.8 100.0 19.58 14.7 27.80
## 110 110 No 6-room 15.6 100.0 19.58 14.7 16.65
## 111 111 No 4-room 14.6 95.7 19.58 14.7 29.53
## 112 112 No 5-room 17.8 93.8 19.58 14.7 28.32
## 113 113 No 6-room 15.4 94.9 19.58 14.7 21.45
## 114 114 No 6-room 21.5 97.3 19.58 14.7 14.10
## 115 115 No 5-room 19.6 100.0 19.58 14.7 13.28
## 116 116 Yes 5-room 15.3 88.0 19.58 14.7 12.12
## 117 117 No 6-room 19.4 98.5 19.58 14.7 15.79
## 118 118 Yes 6-room 17.0 96.0 19.58 14.7 15.12
## 119 119 Yes 6-room 15.6 82.6 19.58 14.7 15.02
## 120 120 No 5-room 13.1 94.0 19.58 14.7 16.14
## 121 121 No 7-room 41.3 97.4 19.58 14.7 4.59
## 122 122 No 6-room 24.3 100.0 19.58 14.7 6.43
## 123 123 No 7-room 23.3 100.0 19.58 14.7 7.39
## 124 124 Yes 6-room 27.0 92.6 19.58 14.7 5.50
## 125 125 No 7-room 50.0 90.8 19.58 14.7 1.73
## 126 126 Yes 7-room 50.0 98.2 19.58 14.7 1.92
## 127 127 Yes 7-room 50.0 93.9 19.58 14.7 3.32
## 128 128 No 6-room 22.7 91.8 19.58 14.7 11.64
## 129 129 No 6-room 25.0 93.0 19.58 14.7 9.81
## 130 130 No 7-room 50.0 96.2 19.58 14.7 3.70
## 131 131 No 6-room 23.8 79.2 19.58 14.7 12.14
## 132 132 No 6-room 23.8 96.1 19.58 14.7 11.10
## 133 133 No 6-room 22.3 95.2 19.58 14.7 11.32
## 134 134 No 6-room 17.4 94.6 19.58 14.7 14.43
## 135 135 No 6-room 19.1 97.3 19.58 14.7 12.03
## 136 136 No 6-room 23.1 88.5 4.05 16.6 14.69
## 137 137 No 6-room 23.6 84.1 4.05 16.6 9.04
## 138 138 No 6-room 22.6 68.7 4.05 16.6 9.64
## 139 139 No 7-room 29.4 33.1 4.05 16.6 5.33
## 140 140 No 6-room 23.2 47.2 4.05 16.6 10.11
## 141 141 No 6-room 24.6 73.4 4.05 16.6 6.29
## 142 142 No 7-room 29.9 74.4 4.05 16.6 6.92
## 143 143 No 7-room 37.2 58.4 2.46 17.8 5.04
## 144 144 No 7-room 39.8 83.3 2.46 17.8 7.56
## 145 145 No 6-room 36.2 62.2 2.46 17.8 9.45
## 146 146 No 7-room 37.9 92.2 2.46 17.8 4.82
## 147 147 No 7-room 32.5 95.6 2.46 17.8 5.68
## 148 148 No 6-room 26.4 89.8 2.46 17.8 13.98
## 149 149 No 6-room 29.6 68.8 2.46 17.8 13.15
## 150 150 No 7-room 50.0 53.6 2.46 17.8 4.45
## 151 151 No 6-room 22.6 22.3 10.59 18.6 10.87
## 152 152 No 6-room 24.4 52.5 10.59 18.6 10.97
## 153 153 No 6-room 22.5 72.7 10.59 18.6 18.06
## 154 154 Yes 6-room 24.4 59.1 10.59 18.6 14.66
## 155 155 Yes 5-room 20.0 100.0 10.59 18.6 23.09
## 156 156 Yes 6-room 21.7 92.1 10.59 18.6 17.27
## 157 157 Yes 5-room 19.3 88.6 10.59 18.6 23.98
## 158 158 Yes 6-room 22.4 53.8 10.59 18.6 16.03
## 159 159 No 6-room 28.1 32.3 10.59 18.6 9.38
## 160 160 No 5-room 23.7 9.8 10.59 18.6 29.55
## 161 161 No 6-room 25.0 42.4 10.59 18.6 9.47
## 162 162 Yes 6-room 23.3 56.0 13.89 16.4 13.51
## 163 163 No 7-room 28.7 85.1 13.89 16.4 9.69
## 164 164 Yes 6-room 21.5 93.8 13.89 16.4 17.92
## 165 165 Yes 6-room 23.0 92.4 13.89 16.4 10.50
## 166 166 Yes 7-room 26.7 88.5 6.20 17.4 9.71
## 167 167 Yes 6-room 21.7 91.3 6.20 17.4 21.46
## 168 168 Yes 7-room 27.5 77.7 6.20 17.4 9.93
## 169 169 No 7-room 30.1 80.8 6.20 17.4 7.60
## 170 170 No 7-room 44.8 78.3 6.20 17.4 4.14
## 171 171 No 7-room 50.0 83.0 6.20 17.4 4.63
## 172 172 No 7-room 37.6 86.5 6.20 17.4 3.13
## 173 173 No 7-room 31.6 79.9 6.20 17.4 6.36
## 174 174 No 7-room 46.7 17.0 6.20 17.4 3.92
## 175 175 No 7-room 31.5 21.4 6.20 17.4 3.76
## 176 176 No 6-room 24.3 68.1 6.20 17.4 11.65
## 177 177 No 7-room 31.7 76.9 6.20 17.4 5.25
## 178 178 No 7-room 41.7 73.3 6.20 17.4 2.47
## 179 179 No 7-room 48.3 70.4 6.20 17.4 3.95
## 180 180 Yes 7-room 29.0 66.5 6.20 17.4 8.05
## 181 181 No 6-room 24.0 61.5 6.20 17.4 10.88
## 182 182 Yes 7-room 25.1 76.5 6.20 17.4 9.54
## 183 183 No 7-room 31.5 71.6 6.20 17.4 4.73
## 184 184 No 6-room 23.9 18.4 13.92 16.0 8.58
## 185 185 No 6-room 21.7 42.3 13.92 16.0 10.40
## 186 186 No 7-room 28.6 31.1 13.92 16.0 6.27
## 187 187 No 7-room 27.1 51.0 13.92 16.0 7.39
## 188 188 No 6-room 20.3 58.0 13.92 16.0 15.84
## 189 189 No 7-room 22.8 82.5 9.90 18.4 4.54
## 190 190 No 6-room 20.3 76.7 9.90 18.4 9.97
## 191 191 No 4-room 16.1 37.8 9.90 18.4 12.64
## 192 192 No 6-room 22.1 52.8 9.90 18.4 5.98
## 193 193 No 6-room 19.4 90.4 9.90 18.4 11.72
## 194 194 No 6-room 21.6 82.8 9.90 18.4 7.90
## 195 195 No 7-room 23.8 87.3 9.90 18.4 9.28
## 196 196 No 6-room 16.2 77.7 9.90 18.4 11.50
## 197 197 No 6-room 17.8 83.2 9.90 18.4 18.33
## 198 198 No 6-room 19.8 71.7 9.90 18.4 15.94
## 199 199 No 6-room 23.1 67.2 9.90 18.4 10.36
## 200 200 No 6-room 21.0 58.8 9.90 18.4 12.73
## 201 201 No 6-room 23.8 52.3 7.38 19.6 7.20
## 202 202 No 6-room 23.1 54.3 7.38 19.6 6.87
## 203 203 No 6-room 20.4 49.9 7.38 19.6 7.70
## 204 204 No 6-room 18.5 74.3 7.38 19.6 11.74
## 205 205 No 6-room 25.0 40.1 7.38 19.6 6.12
## 206 206 No 6-room 24.6 14.7 7.38 19.6 5.08
## 207 207 No 6-room 23.0 28.9 7.38 19.6 6.15
## 208 208 No 6-room 22.2 43.7 7.38 19.6 12.79
## 209 209 No 6-room 19.3 25.8 3.24 16.9 9.97
## 210 210 No 6-room 22.6 17.2 3.24 16.9 7.34
## 211 211 No 6-room 19.8 32.2 3.24 16.9 9.09
## 212 212 No 6-room 22.2 38.1 5.19 20.2 5.68
## 213 213 No 6-room 20.7 38.5 5.19 20.2 6.75
## 214 214 No 6-room 21.1 34.5 5.19 20.2 8.01
## 215 215 No 6-room 19.5 46.3 5.19 20.2 9.80
## 216 216 No 6-room 18.5 59.6 5.19 20.2 10.56
## 217 217 No 6-room 20.6 37.3 5.19 20.2 8.51
## 218 218 No 6-room 19.0 45.4 5.19 20.2 9.74
## 219 219 No 6-room 18.7 58.5 5.19 20.2 9.29
## 220 220 No 7-room 16.5 59.7 1.89 15.9 8.65
## 221 221 No 6-room 17.5 48.5 4.39 18.8 10.53
## 222 222 No 6-room 17.2 52.3 4.39 18.8 12.67
## 223 223 Yes 6-room 17.8 97.4 18.10 20.2 17.60
## 224 224 Yes 6-room 21.7 91.0 18.10 20.2 13.27
## 225 225 Yes 6-room 22.7 83.4 18.10 20.2 11.48
## 226 226 No 6-room 22.6 81.3 18.10 20.2 12.67
## 227 227 No 6-room 25.0 88.0 18.10 20.2 7.79
## 228 228 No 6-room 19.9 91.1 18.10 20.2 14.19
## 229 229 No 5-room 20.8 96.2 18.10 20.2 10.19
## 230 230 Yes 6-room 16.8 89.0 18.10 20.2 14.64
## 231 231 Yes 7-room 21.9 82.9 18.10 20.2 5.29
## 232 232 No 4-room 27.5 87.9 18.10 20.2 7.12
## 233 233 No 4-room 21.9 91.4 18.10 20.2 14.00
## 234 234 No 4-room 23.1 100.0 18.10 20.2 13.33
## 235 235 No 4-room 50.0 100.0 18.10 20.2 3.26
## 236 236 Yes 7-room 50.0 96.8 18.10 20.2 3.73
## 237 237 Yes 7-room 50.0 97.5 18.10 20.2 2.96
## 238 238 No 6-room 50.0 100.0 18.10 20.2 9.53
## 239 239 Yes 6-room 50.0 89.6 18.10 20.2 8.88
## 240 240 No 4-room 13.8 100.0 18.10 20.2 34.77
## 241 241 No 4-room 13.8 100.0 18.10 20.2 37.97
## 242 242 No 7-room 15.0 97.9 18.10 20.2 13.44
## 243 243 No 7-room 13.9 93.3 18.10 20.2 23.24
## 244 244 No 7-room 13.3 98.8 18.10 20.2 21.24
## 245 245 No 6-room 13.1 96.2 18.10 20.2 23.69
## 246 246 No 6-room 10.2 100.0 18.10 20.2 21.78
## 247 247 No 7-room 10.4 91.9 18.10 20.2 17.21
## 248 248 No 7-room 10.9 99.1 18.10 20.2 21.08
## 249 249 No 6-room 11.3 100.0 18.10 20.2 23.60
## 250 250 No 6-room 12.3 100.0 18.10 20.2 24.56
## 251 251 No 4-room 8.8 91.2 18.10 20.2 30.63
## 252 252 No 5-room 7.2 98.1 18.10 20.2 30.81
## 253 253 No 4-room 10.5 100.0 18.10 20.2 28.28
## 254 254 No 5-room 7.4 89.5 18.10 20.2 31.99
## 255 255 No 4-room 10.2 100.0 18.10 20.2 30.62
## 256 256 No 5-room 11.5 98.9 18.10 20.2 20.85
## 257 257 No 6-room 15.1 97.0 18.10 20.2 17.11
## 258 258 No 6-room 23.2 82.5 18.10 20.2 18.76
## 259 259 No 5-room 9.7 97.0 18.10 20.2 25.68
## 260 260 No 6-room 13.8 92.6 18.10 20.2 15.17
## 261 261 No 6-room 12.7 94.7 18.10 20.2 16.35
## 262 262 No 6-room 13.1 98.8 18.10 20.2 17.12
## 263 263 No 6-room 12.5 96.0 18.10 20.2 19.37
## 264 264 No 6-room 8.5 98.9 18.10 20.2 19.92
## 265 265 No 5-room 5.0 100.0 18.10 20.2 30.59
## 266 266 No 6-room 6.3 77.8 18.10 20.2 29.97
## 267 267 No 6-room 5.6 100.0 18.10 20.2 26.77
## 268 268 No 6-room 7.2 100.0 18.10 20.2 20.32
## 269 269 No 6-room 12.1 100.0 18.10 20.2 20.31
## 270 270 No 5-room 8.3 96.0 18.10 20.2 19.77
## 271 271 No 6-room 8.5 85.4 18.10 20.2 27.38
## 272 272 No 6-room 5.0 100.0 18.10 20.2 22.98
## 273 273 No 4-room 11.9 100.0 18.10 20.2 23.34
## 274 274 No 6-room 27.9 100.0 18.10 20.2 12.13
## 275 275 No 6-room 17.2 97.9 18.10 20.2 26.40
## 276 276 No 7-room 27.5 100.0 18.10 20.2 19.78
## 277 277 No 6-room 15.0 100.0 18.10 20.2 10.11
## 278 278 No 7-room 17.2 100.0 18.10 20.2 21.22
## 279 279 No 4-room 17.9 100.0 18.10 20.2 34.37
## 280 280 No 5-room 16.3 100.0 18.10 20.2 20.08
## 281 281 No 4-room 7.0 100.0 18.10 20.2 36.98
## 282 282 No 6-room 7.2 100.0 18.10 20.2 29.05
## 283 283 No 7-room 7.5 90.8 18.10 20.2 25.79
## 284 284 No 5-room 10.4 89.1 18.10 20.2 26.64
## 285 285 No 6-room 8.8 100.0 18.10 20.2 20.62
## 286 286 No 7-room 8.4 76.5 18.10 20.2 22.74
## 287 287 No 6-room 16.7 100.0 18.10 20.2 15.02
## 288 288 No 6-room 14.2 95.3 18.10 20.2 15.70
## 289 289 No 6-room 20.8 87.6 18.10 20.2 14.10
## 290 290 No 6-room 13.4 85.1 18.10 20.2 23.29
## 291 291 No 6-room 11.7 70.6 18.10 20.2 17.16
## 292 292 No 6-room 8.3 95.4 18.10 20.2 24.39
## 293 293 No 6-room 10.2 59.7 18.10 20.2 15.69
## 294 294 No 6-room 10.9 78.7 18.10 20.2 14.52
## 295 295 No 6-room 11.0 78.1 18.10 20.2 21.52
## 296 296 No 6-room 9.5 95.6 18.10 20.2 24.08
## 297 297 No 6-room 14.5 86.1 18.10 20.2 17.64
## 298 298 No 7-room 14.1 94.3 18.10 20.2 19.69
## 299 299 No 6-room 16.1 74.8 18.10 20.2 12.03
## 300 300 No 6-room 14.3 87.9 18.10 20.2 16.22
## 301 301 No 6-room 11.7 95.0 18.10 20.2 15.17
## 302 302 No 7-room 13.4 94.6 18.10 20.2 23.27
## 303 303 No 6-room 9.6 93.3 18.10 20.2 18.05
## 304 304 No 6-room 8.7 100.0 18.10 20.2 26.45
## 305 305 No 6-room 8.4 87.9 18.10 20.2 34.02
## 306 306 No 6-room 12.8 93.9 18.10 20.2 22.88
## 307 307 No 6-room 10.5 92.4 18.10 20.2 22.11
## 308 308 No 6-room 17.1 97.2 18.10 20.2 19.52
## 309 309 No 6-room 18.4 100.0 18.10 20.2 16.59
## 310 310 No 6-room 15.4 100.0 18.10 20.2 18.85
## 311 311 No 6-room 10.8 96.6 18.10 20.2 23.79
## 312 312 No 6-room 11.8 94.8 18.10 20.2 23.98
## 313 313 No 6-room 14.9 96.4 18.10 20.2 17.79
## 314 314 No 6-room 12.6 96.6 18.10 20.2 16.44
## 315 315 No 6-room 14.1 98.7 18.10 20.2 18.13
## 316 316 No 6-room 13.0 98.3 18.10 20.2 19.31
## 317 317 No 7-room 13.4 92.6 18.10 20.2 17.44
## 318 318 No 7-room 15.2 98.2 18.10 20.2 17.73
## 319 319 No 6-room 16.1 91.8 18.10 20.2 17.27
## 320 320 No 7-room 17.8 99.3 18.10 20.2 16.74
## 321 321 No 7-room 14.9 94.1 18.10 20.2 18.71
## 322 322 No 7-room 14.1 86.5 18.10 20.2 18.13
## 323 323 No 6-room 12.7 87.9 18.10 20.2 19.01
## 324 324 No 6-room 13.5 80.3 18.10 20.2 16.94
## 325 325 No 6-room 14.9 83.7 18.10 20.2 16.23
## 326 326 No 6-room 20.0 84.4 18.10 20.2 14.70
## 327 327 No 7-room 16.4 90.0 18.10 20.2 16.42
## 328 328 No 6-room 17.7 88.4 18.10 20.2 14.65
## 329 329 No 6-room 19.5 83.0 18.10 20.2 13.99
## 330 330 No 7-room 20.2 89.9 18.10 20.2 10.29
## 331 331 No 6-room 21.4 65.4 18.10 20.2 13.22
## 332 332 No 6-room 19.9 48.2 18.10 20.2 14.13
## 333 333 No 6-room 19.0 84.7 18.10 20.2 17.15
## 334 334 No 6-room 19.1 94.5 18.10 20.2 21.32
## 335 335 No 6-room 19.1 71.0 18.10 20.2 18.13
## 336 336 No 6-room 20.1 56.7 18.10 20.2 14.76
## 337 337 No 6-room 19.9 84.0 18.10 20.2 16.29
## 338 338 No 6-room 19.6 90.7 18.10 20.2 12.87
## 339 339 No 6-room 23.2 75.0 18.10 20.2 14.36
## 340 340 No 7-room 29.8 67.6 18.10 20.2 11.66
## 341 341 No 5-room 13.8 95.4 18.10 20.2 18.14
## 342 342 No 6-room 13.3 97.4 18.10 20.2 24.10
## 343 343 No 6-room 16.7 93.6 18.10 20.2 18.68
## 344 344 No 5-room 12.0 97.3 18.10 20.2 24.91
## 345 345 No 6-room 14.6 96.7 18.10 20.2 18.03
## 346 346 No 6-room 21.4 88.0 18.10 20.2 13.11
## 347 347 No 6-room 23.0 64.7 18.10 20.2 10.74
## 348 348 No 7-room 23.7 74.9 18.10 20.2 7.74
## 349 349 No 7-room 25.0 77.0 18.10 20.2 7.01
## 350 350 No 6-room 21.8 40.3 18.10 20.2 10.42
## 351 351 No 6-room 20.6 41.9 18.10 20.2 13.34
## 352 352 No 6-room 21.2 51.9 18.10 20.2 10.58
## 353 353 No 6-room 19.1 79.8 18.10 20.2 14.98
## 354 354 No 6-room 20.6 53.2 18.10 20.2 11.45
## 355 355 No 5-room 15.2 92.7 27.74 20.1 18.06
## 356 356 No 5-room 7.0 98.3 27.74 20.1 23.97
## 357 357 No 5-room 8.1 98.0 27.74 20.1 29.68
## 358 358 No 6-room 13.6 98.8 27.74 20.1 18.07
## 359 359 No 6-room 20.1 83.5 27.74 20.1 13.35
## 360 360 No 6-room 21.8 54.0 9.69 19.2 12.01
## 361 361 No 6-room 24.5 42.6 9.69 19.2 13.59
## 362 362 No 6-room 23.1 28.8 9.69 19.2 17.60
## 363 363 No 5-room 19.7 72.9 9.69 19.2 21.14
## 364 364 No 6-room 18.3 70.6 9.69 19.2 14.10
## 365 365 No 6-room 21.2 65.3 9.69 19.2 12.92
## 366 366 No 6-room 17.5 73.5 9.69 19.2 15.10
## 367 367 No 6-room 16.8 79.7 9.69 19.2 14.33
## 368 368 No 7-room 22.4 69.1 11.93 21.0 9.67
## 369 369 No 6-room 20.6 76.7 11.93 21.0 9.08
## 370 370 No 7-room 23.9 91.0 11.93 21.0 5.64
## 371 371 No 7-room 22.0 89.3 11.93 21.0 6.48
## 372 372 No 6-room 11.9 80.8 11.93 21.0 7.88Number of variables and variable names
dim(housing_prices)## [1] 372 8names(housing_prices)## [1] "ID" "river" "rooms" "price" "age" "industry" "ptratio"
## [8] "low_ses"Present the study design, null and alternative hypotheses (5%)
Study Design: The cross-sectional investigation of 372 suburbs to determine whether there was variation in housing prices based on the number of rooms in houses.
Null Hypothesis (H0): There is no significant difference in median housing prices among houses with different numbers of rooms. Alternative Hypothesis (Ha): Median housing prices vary significantly among houses with different numbers of rooms.
Describe the characteristics of the study sample by the number of rooms/house (10%)
library(table1)##
## Attaching package: 'table1'## The following objects are masked from 'package:base':
##
## units, units<-table1(~ price + river + age + industry + ptratio + low_ses | rooms, data = housing_prices)| 4-room (N=15) |
5-room (N=27) |
6-room (N=254) |
7-room (N=76) |
Overall (N=372) |
|
|---|---|---|---|---|---|
| price | |||||
| Mean (SD) | 17.3 (10.7) | 14.0 (5.05) | 18.9 (5.50) | 28.8 (11.7) | 20.5 (8.59) |
| Median [Min, Max] | 13.8 [7.00, 50.0] | 14.4 [5.00, 23.7] | 19.4 [5.00, 50.0] | 27.5 [7.50, 50.0] | 19.8 [5.00, 50.0] |
| river | |||||
| No | 15 (100%) | 23 (85.2%) | 239 (94.1%) | 67 (88.2%) | 344 (92.5%) |
| Yes | 0 (0%) | 4 (14.8%) | 15 (5.9%) | 9 (11.8%) | 28 (7.5%) |
| age | |||||
| Mean (SD) | 93.5 (15.9) | 89.8 (20.4) | 75.6 (24.3) | 77.2 (21.1) | 77.7 (23.6) |
| Median [Min, Max] | 100 [37.8, 100] | 96.2 [9.80, 100] | 84.5 [6.00, 100] | 82.7 [2.90, 100] | 87.3 [2.90, 100] |
| industry | |||||
| Mean (SD) | 17.8 (2.23) | 17.7 (5.43) | 13.6 (6.16) | 11.1 (6.53) | 13.5 (6.32) |
| Median [Min, Max] | 18.1 [9.90, 19.6] | 18.1 [6.91, 27.7] | 13.9 [2.18, 27.7] | 9.90 [1.89, 19.6] | 18.1 [1.89, 27.7] |
| ptratio | |||||
| Mean (SD) | 19.3 (1.94) | 18.7 (2.31) | 19.3 (1.71) | 18.4 (1.81) | 19.1 (1.82) |
| Median [Min, Max] | 20.2 [14.7, 20.2] | 20.1 [14.7, 21.2] | 20.2 [14.7, 21.2] | 18.0 [14.7, 21.0] | 20.2 [14.7, 21.2] |
| low_ses | |||||
| Mean (SD) | 24.4 (11.4) | 23.3 (6.75) | 14.5 (5.37) | 9.14 (6.25) | 14.4 (7.15) |
| Median [Min, Max] | 29.3 [3.26, 38.0] | 24.0 [10.2, 34.4] | 14.1 [5.08, 34.0] | 6.79 [1.73, 25.8] | 13.6 [1.73, 38.0] |
Develop and interpret a histogram for the distribution of house prices (10%)
library(ggplot2)
library(grid)
library(gridExtra)
library(dplyr)##
## Attaching package: 'dplyr'## The following object is masked from 'package:gridExtra':
##
## combine## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(GGally)## Registered S3 method overwritten by 'GGally':
## method from
## +.gg ggplot2library(ggthemes)
p = ggplot(data = housing_prices, aes(x = price)) + geom_histogram(color = "black", fill = "light blue") + labs(x = "Median housing prices (x USD 1,000)") + labs(y = "Count number")
p1 = ggplot(data = housing_prices, aes(x = price, y = ..density..)) + geom_histogram(color = "black", fill = "light blue") + geom_density(col="red") + labs(x = "Median housing prices (x USD 1,000)") + labs(y = "Density")
grid.arrange(p, p1, nrow = 1.5, top = textGrob("Distribution of house prices", gp = gpar(fontsize = 18, font = 2)))## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.## Warning: The dot-dot notation (`..density..`) was deprecated in ggplot2 3.4.0.
## ℹ Please use `after_stat(density)` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
Develop and interpret a box plot to describe the differences in housing prices among the number of rooms per household (10%)
p = ggplot(data = housing_prices, aes(x = rooms, y = price, fill = rooms, col = rooms))
p1 = p + geom_boxplot(col = "black") + geom_jitter(alpha = 0.01) + labs(x = "Room numbers of each household", y = "Median housing prices (x USD 1,000)") + ggtitle("Box Plot of housing prices by room numbers of each household") + theme_bw()
p1
Conduct a statistical test to determine whether housing prices were different among houses with different numbers of rooms. Interpret the findings (15%)
Kruskal-Wallis test
kruskal.test(price ~ rooms, data = housing_prices)##
## Kruskal-Wallis rank sum test
##
## data: price by rooms
## Kruskal-Wallis chi-squared = 75.504, df = 3, p-value = 2.826e-16ANOVA test
anova_test= aov(price ~ rooms, data = housing_prices)
summary(anova_test)## Df Sum Sq Mean Sq F value Pr(>F)
## rooms 3 7162 2387.2 43.49 <2e-16 ***
## Residuals 368 20202 54.9
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1The Kruskal-Wallis and ANOVA tests given p-value of approximately zero (2.826e-16 and 2e-16), P-value < 0.05. Therefore, null hypothesis (H0) in favor of the alternative hypothesis (Ha) is rejected.
In conclusion, there are significant differences in housing prices among houses with different numbers of rooms.
Determine which particular number of rooms/house had different house prices using the Tukey posthoc test. Fill in the following table and interpret the findings (20%)
tukey_result = TukeyHSD(anova_test)
tukey_result## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = price ~ rooms, data = housing_prices)
##
## $rooms
## diff lwr upr p adj
## 5-room-4-room -3.215556 -9.373321 2.942210 0.5331459
## 6-room-4-room 1.603780 -3.477109 6.684668 0.8475492
## 7-room-4-room 11.511053 6.108559 16.913546 0.0000004
## 6-room-5-room 4.819335 0.948716 8.689954 0.0077590
## 7-room-5-room 14.726608 10.442544 19.010672 0.0000000
## 7-room-6-room 9.907273 7.407162 12.407384 0.0000000tukey_results <- data.frame(
Comparisons = c("5-room houses vs. 4-room houses","6-room houses vs. 4-room houses", "7-room houses vs. 4-room houses", "6-room houses vs. 5-room houses", "7-room houses vs. 5-room houses", "7-room houses vs. 6-room houses"),
Mean_Differences_in_housing_price= c("-3.21 (-9.37, 2.94)","1.60 [-3.48, 6.68]","11.51 [6.11, 16.91]","4.82 [0.95, 8.69]","14.73 [10.44, 19.01]","9.91 [7.41, 12.41]"),
P_Value = c("0.5331", "0.8475", "0.0000", "0.0078", "0.0000", "0.0000")
)
print(tukey_results, row.names = FALSE)## Comparisons Mean_Differences_in_housing_price P_Value
## 5-room houses vs. 4-room houses -3.21 (-9.37, 2.94) 0.5331
## 6-room houses vs. 4-room houses 1.60 [-3.48, 6.68] 0.8475
## 7-room houses vs. 4-room houses 11.51 [6.11, 16.91] 0.0000
## 6-room houses vs. 5-room houses 4.82 [0.95, 8.69] 0.0078
## 7-room houses vs. 5-room houses 14.73 [10.44, 19.01] 0.0000
## 7-room houses vs. 6-room houses 9.91 [7.41, 12.41] 0.0000The Tukey posthoc test shows that houses with 7 rooms had significant differencess in housing price (P-value ≈ 0 <0.05) compared to the ones of 4, 5 and 6 rooms. Similar manner is found when comparing houses with 6 rooms to those with 5 rooms (P-value = 0.0078 <0.05).
On the contrary, in case of comparing the houses with 5 and 6 rooms to the house with 5 rooms, there are no statistically significant differences in house prices (P-value=0.53 and 0.85 > 0.05).